如何用matlab计算分形维数
时间: 2023-08-08 17:08:10 浏览: 122
计算分形维数可以采用盒计数法(Box counting method),以下是 MATLAB 的示例代码:
1. 生成分形图形
```matlab
% 生成分形图形
N = 10000;
x = zeros(N,1);
y = zeros(N,1);
x(1) = 0;
y(1) = 0;
for i = 2:N
r = rand;
if r < 0.01
x(i) = 0.5 * x(i-1) - 0.1 * y(i-1);
y(i) = 0.1 * x(i-1) + 0.5 * y(i-1) + 1.0;
elseif r < 0.86
x(i) = 0.85 * x(i-1) + 0.04 * y(i-1);
y(i) = -0.04 * x(i-1) + 0.85 * y(i-1) + 1.6;
elseif r < 0.93
x(i) = 0.2 * x(i-1) - 0.26 * y(i-1);
y(i) = 0.23 * x(i-1) + 0.22 * y(i-1) + 1.6;
else
x(i) = -0.15 * x(i-1) + 0.28 * y(i-1);
y(i) = 0.26 * x(i-1) + 0.24 * y(i-1) + 0.44;
end
end
plot(x,y,'.','MarkerSize',1)
axis equal
```
2. 计算盒计数
```matlab
% 计算盒计数
L = 10;
M = 100;
counts = zeros(M,1);
for i = 1:M
N = 2^(i-1);
boxes = zeros(N,N);
for j = 1:length(x)
ix = floor((x(j) + 1.5) * N / L);
iy = floor((y(j) + 0.5) * N / L);
if ix > 0 && ix <= N && iy > 0 && iy <= N
boxes(iy,ix) = 1;
end
end
counts(i) = sum(sum(boxes)) / (N*N);
end
```
3. 绘制盒计数图
```matlab
% 绘制盒计数图
log_counts = log(counts);
log_scale = log(L./2.^(0:M-1)');
p = polyfit(log_scale,log_counts,1);
D = p(1);
hold on
plot(log_scale,polyval(p,log_scale),'r')
text(2,6,sprintf('D = %f',D))
```
其中,L 表示盒子的尺寸,M 表示盒子的数量。这段代码生成一个分形图形,然后计算不同尺寸的盒子所能覆盖的分形图形的面积比例,最后根据盒子的尺寸和面积比例计算分形维数 D。